Application Research Of Deep Learning And Compressed Sensing In Gravity And Magnetic Background Field Construction

The construction of high precision and high resolution gravity and magnetic background field is one of the hot topics in gravity and magnetic assisted navigation.With the emergence of the present all kinds of new algorithm,the algorithm theory and application of interdisciplinary research development,this paper mainly based on the deep learning algorithm and the compressed sensing theory to study the gravity and magnetic data interpolation reconstruction,gradient data calculation,potential field continuation,etc,to solve the problem of the construction of gravity and magnetic background field has carried on the beneficial exploration.The main research contents and innovations are as follows:(1)The theories of gravity and magnetic background field construction,deep learning and compressed sensing are introduced.According to the research focus and demand of gravity and magnetic background field construction,in terms of data acquisition,the Stokes formula is introduced to calculate the gravity gradient full tensor under spherical approximation.In terms of data processing,the principle of potential field downward continuation and the idea of derivative iteration are introduced.In terms of grid mapping,four traditional methods are introduced.In terms of deep learning algorithm,classical neural network model,activation function and loss function commonly used in network structure,and optimization algorithm of network training are introduced.Finally,in terms of compressed sensing theory,the sparse basis,observation matrix and reconstruction algorithm selected for sparse reconstruction are introduced,which provides theoretical support for deep learning algorithm and application research of compressed sensing theory in subsequent chapters.(2)Aiming at the problem that the accuracy of gravity measurement data will be reduced in the process of interpolation and reconstruction,a method of BP neural network optimization based on particle swarm optimization algorithm is proposed and applied to the estimation of gravity data.The results of PSO-BP neural network,ordinary BP network and traditional Kriging method on gravity anomaly interpolation are compared and analyzed by simulation experiments.It is found that this method has certain advantages in mean square error and difference stability,but it takes a long time to calculate.The PSO-BP neural network is trained with gravity observation data in central Australia,and the experimental results show that the interpolation effect of this method is better than that of BP neural network and Kriging method in the whole region.The addition of elevation data as the input of PSO-BP neural network can further improve the accuracy of this method in predicting gravity anomaly field.Finally,the low-frequency gravity field of gravity anomaly field estimated by different methods is constructed based on wavelet transform.From the results,the low-frequency information of gravity background field constructed by this method based on the same amount of data is closer to the real field information.(3)Aiming at the problem of low estimation accuracy of geomagnetic data under the condition of low sampling rate,the compressed sensing algorithm of subspace tracing(SP)algorithm as reconstruction algorithm,discrete cosine matrix as sparse basis and Gaussian random matrix as observation matrix is proposed.Based on the measured magnetic data of central Australia and the statistical characteristics of the data,the ability of this method and other methods in the construction of high precision geomagnetic maps is discussed.The results show that the deterministic method and geostatistical method reflect the spatial structure characteristics of geomagnetic data distribution based on mathematical function and variogram,and can obtain decent interpolation results at various sampling rates.Under the condition of low sampling rate,the compressive sensing algorithm has the strongest interpolation ability,and the root mean square error is 14.41 n T in the experiment,which improves the accuracy about 38.5% compared with the Universal Kriging method.With the increase of sample training data,the accuracy of neural network algorithm increases the most.When the sampling rate is 10% to 30%,the root mean square error decreases from 72.85 n T to 14.38 n T.(4)Aiming at the calculation problem of constructing gravity gradient field by using gravity anomaly data,a nonlinear mapping network Gra Com Net model method was constructed based on full convolutional neural network.Based on the characteristics of the problem,the network structure with corresponding depth was designed.The sample data set was formed by using the gravity anomaly and gravity gradient data of cuboid forward modeling.Appropriate network parameters and optimization algorithms are selected to learn and train the network,and the end-to-end neural network model from gravity anomaly grid data to gravity gradient tensor data in the corresponding range is finally completed.Two typical models are used to verify the effect of network prediction.Experimental results show that: Gra Com Net neural network can calculate the gravity gradient full tensor grid in the central range from the gravity anomaly grid data in the region.The standard deviation of the network prediction results of model 1 and combined model2 are all below 0.7mgal.The network prediction values are in good agreement with the data trend of the theoretical gravity gradient tensor.After adding noise,the network shows good anti-noise performance and generalization performance.(5)Aiming at the problem of discomfort and noise accumulation in the downward continuation of traditional potential field,put forward the U-Net network method.Several magnetic anomaly data of different heights generated by the sphere model are taken as sample data sets,using the up and down sampling coding process to extract the characteristics of the magnetic field data,studied the magnetic field data of different height and surface data of mapping relation,A U-Net neural network model was established to realize downward continuation of magnetic field data,and the traditional derivative iterative method was used to conduct comparative analysis experiments.The results show that: The accuracy of U-Net network method reached 1.1939 n T,1.5313 n T and 1.6831 n T respectively at 200 m,500m and800 m downward continuation height,which increased 35.4%,37.7% and 70.3% respectively compared with the derivative iteration method at the same height.After adding 3n T mean square error random noise,the standard deviation of the continuation result of U-Net network method is still below 3n T,showing good anti-noise ability.